Wide Binaries
Untested — Self-Eliminating — Pending External Adjudication (2026)Wide binary star systems — two stars orbiting each other at separations of thousands of AU — provide one of the cleanest tests of gravity in the low-acceleration regime. Synchronism's prediction for them depends on which version of its coherence function you use, and for the density-keyed version, on a number the framework never fixed. This page sets out the versions and what each one predicts.
Why Wide Binaries?
At separations greater than ~104 AU (roughly 0.05 parsecs), the gravitational acceleration between two stars drops below a₀ ≈ 1.2 × 10−10m/s². In Newtonian gravity, nothing special happens. In MOND, orbital velocities should be higher than Newtonian predictions. The anomaly — if it exists — should be visible in the orbital dynamics.
The beauty of wide binaries is simplicity: two gravitating masses, no dark matter halo ambiguity, no complex baryonic physics. It is the closest thing to a clean two-body test of modified gravity.
What MOND predicts
MOND's wide-binary prediction depends on location. A binary in the Solar neighbourhood also sits in the Milky Way's own field, about 1.8 a₀. That external field partly suppresses the boost (the External Field Effect, EFE). With it, AQUAL and QUMOND predict a 1.0–1.4× boost in gravity at low internal acceleration, depending on the treatment. That is up to about +18% in velocity (√1.4 ≈ 1.18), the ~20% signal the Chae vs Banik dispute below is about. Without the EFE the boost would be several times larger: with the simple interpolating function at an internal acceleration of 0.1 a₀, about 3.7× in gravity, or roughly +90% in velocity. (Corrected 2026-09-24: this paragraph used to call the ~18% the no-EFE figure. It is the EFE-included one.)
Synchronism's Prediction: Two Versions
Acceleration-keyed version (the one that fits galaxies)
At its SPARC fit this version is Milgrom's simple MOND function, so it predicts MOND's wide-binary boost, EFE included. Here the test cannot separate it from MOND. It can only fail both together.
Density-keyed version (the headline equation)
Here gravity is boosted by 1/C(ρ), where ρ is the local density. The boost does not depend on the binary's internal acceleration at all, so wide binaries are not special: whatever boost holds at the local density applies to every orbit there. Its size depends on the knee ρcrit. At the solar-neighbourhood density ρ ≈ 0.09 M☉/pc³ the velocity excess over Newton is:
- Published calibration ρcrit = 0.029·V² = 1.5×10³ M☉/pc³ (Milky Way, γ = 0.489): +1.8×10⁴%. That is a factor ~3.5×10⁴ in g, excluded by the Oort limit by orders of magnitude. (Planetary ephemerides cannot see a boost that is uniform across the Solar System, because it is degenerate with the Sun's GM. They constrain only its variation, so they bite only if density is read pointwise, not smoothed over ≥ 30 AU.)
- Measured velocity-blind knee, 0.161 M☉/pc³: +116% (γ = 0.489) or +18.6% (γ = 2).
- Refracted Gravity's elliptical-galaxy knee, 0.0083 M☉/pc³: +9.4% (γ = 0.489) or +0.005% (γ = 2).
- A near-Newtonian 0.05–0.4% needs a knee between 3.8×10⁻⁵ and 3.2×10⁻⁴ M☉/pc³ (γ = 0.489). No other page uses a knee in that window, and it starts where the knee range ruled out on SPARC ends.
The static amplitude is not the only handle: a density-keyed boost changes with time (explorer, 2026-09-23). Everything in one neighbourhood shares the same boost, so a ratio taken at one instant cancels it. That is why TEST-02 reads “γg ≡ 1” for this version. But the Sun moves through the Galactic disc and past nearby stars (α Cen is closing at 22 km/s), so the local density, and with it Geff = G/C(ρ), changes now. Lunar laser ranging measures Ġ/G = (7.1 ± 7.6)×10⁻¹⁴ per year (Hofmann & Müller 2018). With density smoothed over 1–10 pc, the scale the galaxy fits need, the knee grid used on this site predicts 10⁻⁸–10⁻⁵ per year. 68 of 74 laws are excluded against a bound loosened 13×, including all eight near-Newtonian windows of the kind in the last bullet above that the TEST-02 card lists. The survivors are laws that are Newtonian to 10⁻⁸ at the Sun, so they predict nothing here. Pre-registered (site commit 80b8c9c) before the script existed. This is a second, SPARC-independent root for the density-keyed kill, not a new refutation, and it does not touch the acceleration-keyed version. Finding: explorer/findings/density-keyed-C-is-a-moving-G-lunar-laser-ranging-excludes-it-at-pc-smoothing.md.
Arithmetic: maintainer/scripts/test02_amplitude_is_knee_conditional.py and its output file; details on Tier 1, TEST-02.
The Data
The European Space Agency's Gaia mission (Data Release 3) provides the necessary measurements: positions, proper motions, parallaxes, and radial velocities for over a billion stars. From this, wide binary candidates can be identified and their orbital dynamics characterized. Gaia Archive (ESA) →
What the Density-Keyed Version Leaves Testable
Why isn't the local exclusion booked as a refutation? This is not because it is weak. It is cleaner than TEST-09's 3.3σ. It is a consequence of the knee calibration ρcrit = 0.029·V², and that calibration is already recorded as failed in the research ledger (its velocity exponent is excluded at ~11σ). The site counts executed tests grouped by root. Whether this becomes its own booked result is ledger governance and gates on dp.
Revision note
This box was titled “Feasibility Kill — Signal Below Gaia Systematics”. It said solar-neighbourhood density sits above ρcrit, giving C ≈ 1, a 0.05–0.4% Newtonian null, and a signal ~80× below Gaia's reach. At the published calibration the density sits far below the knee, so C ≈ 3×10⁻⁵ and the boost is maximal. The page also said “Standard MOND predicts the same anomaly regardless of where the binary system is located”, which ignores the External Field Effect. Tier 1 carried the knee-conditional correction from 2026-09-10. It reached this page on 2026-09-17, after a researcher visitor persona found both errors.Current Observational Status (last surveyed 2026-06-23; not re-surveyed since)
The wide-binary debate escalated in 2026. The earlier dispute (sample selection, contamination, statistical cuts) has been superseded by a sharper disagreement:
- Chae et al. 2026 (arXiv:2601.21728): Enlarged RV+speckle-vetted sample of 36 binaries → 4.9σ boost with γ_boost ≈ 1.6 — consistent with MOND. (As summarised in June; the sample cut and significance have not been re-checked against the paper since.)
- Saad & Ting 2026 (arXiv:2603.11015): Reanalyzed the same 36 binaries from Chae et al. 2026 using a hierarchical semi-major-axis fit (replacing geometric deprojection) → γ = 1.12 ± 0.25, Newton-consistent at 0.4σ. The entire anomaly lives in one modeling assumption (orbital deprojection prior).
- Prior generation (2023–2024): Banik et al. (2024), Pittordis & Sutherland (2023), Saurabh & Desmond (2024) all Newtonian-consistent with different cuts.
- Hernandez (2023–2024): Anomalies in projected-velocity statistics; methodology disputed.
Why This Test Cannot Be Decisive (As Currently Formulated)
If anomaly confirmed (Chae wins)
A confirmed EFE-suppressed MOND anomaly would support MOND and the acceleration-keyed version equally. For the density law it would rule out the near-Newtonian knee window. The published calibration is already excluded.
If null confirmed (Banik wins)
The acceleration-keyed version fails together with MOND's simple function. The density law survives only in the near-Newtonian knee window, where it cannot be told apart from Newton.